An Introduction to Quantum Mechanics

The Origins of Quantum Mechanics

Until the end of the nineteenth century, it was thought that atomic and subatomic particles behaved in the same way as much larger objects. Newton's laws of classical mechanics accurately described the motion of everyday objects and planets and it was assumed that the same laws governed the motion of particles such as atoms and electrons.

However, experimental evidence was accumulating to suggest that this was not the case. Inconsistencies were observed by scientists studying black body radiation, heat capacities, atomic and molecular spectra and electromagnetic radiation which suggested that only certain descrete values for the energy of a system are possible. This was in complete contrast to classical mechanics which predicts that there should be no restrictions on the energy which a system can take.

This phenomenon is known as quantization and these observations led to the birth of Quantum Mechanics.

How does Quantum Mechanics work?

The discovery of quantization forced scientists to change the way in which they described matter. Classical physics described matter as particles which travel along definite paths but quantum mechanics requires matter to be described as particles distributed through space like a wave.

This wave is called the wavefunction, Y. It is a mathematical expression which contains all the information known about the particle. The wavefunction can be found by solving the Schrodinger Equation (Erwin Schrodinger, 1926).

The one dimensional, time-independent Schrodinger equation is:

Schrodinger's equation

By entering all the forces acting on the particle, its position in space relative to the other particles with which it is interating and other boundary conditions, such as the space in which the particle is confined, the Schrodinger equation calculates the particle's allowed wavefunctions and corresponding energy levels. Each energy level is defined in terms of a set of quantum numbers.

The Born Interpretation of the Wavefunction

The Born Interpretation of the wavefunction relates to the probability of finding the particle at different positions in space. In one dimension:

If the wavefunction of a particle has the value Y at some point x, the probability of finding the particle between x and x+dx is proportional to |Y|2 dx

Yis called the probability amplitude and |Y|2 is called the probability density

The probability of finding the particle at a given position is not the only information contained in the wavefunction. The wavefunction carries all the information known about the particle. Properties such as the particle's kinetic energy can also be found from the wavefunction.

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Designed by Peter Lewis, Undergraduate, School of Chemistry, University of Bristol.
Email: pl8070@bristol.ac.uk
School of Chemistry, University of Bristol